David Cameron used his New Year's message to declare that Britain is "heading in the right direction" on all the big issues and can look forward to 2013 with "realism and optimism".

In the video address, the Prime Minister acknowledged that 2012 was "tough", with many families finding it difficult to make ends meet, and admitted he had "no quick fixes" to the UK's economic problems.

But he cited evidence of "real progress" on cutting the state deficit, reforming welfare and improving school standards, which he said was preparing Britain to succeed in the "global race" with emerging economic giants like China and India for the jobs and opportunities of the future.

Mr Cameron said that his administration was "a government in a hurry" which would not give in to pressure to slow the pace of deficit reduction or rein in reforms to welfare and education.

The Prime Minister said: "This is my message to the country at the start of 2013. We can look to the future with realism and optimism. Realism, because you can't cure problems that were decades in the making overnight. There are no quick fixes and I wouldn't claim otherwise. But we can be optimistic too because we are making tangible progress. We are doing what's right for our country and what's best for our children's future."

Insisting that "we are on the right track", Mr Cameron said: "On all the big issues that matter to Britain, we are heading in the right direction and I have the evidence to prove it."

The deficit is forecast to be a quarter smaller at the New Year than it was when the coalition Government came to office, there are almost half a million more people in work, and more than 1,000 new academy schools have opened, said Mr Cameron. And he hailed moves to take millions of low-paid workers out of income tax, freeze council tax bills and deliver the largest-ever increase in the state pension.

He said: "This is, quite simply, a government in a hurry. And there's a reason for that. Britain is in a global race to succeed today. It is a race with countries like China, India and Indonesia; a race for the jobs and opportunities of the future.

"So when people say we can slow down on cutting our debts, we are saying no. We can't win in this world with a great millstone of debt round our necks. When people say we've got to stop our welfare reforms because somehow it is cruel to expect people to work, we are saying no. Getting people into good jobs is absolutely vital, not just for them, but for all of us.

Labour vice chair Michael Dugher said: "It's a case of more of the same from David Cameron. In his New Year message, Cameron talks of people who work hard in this country but he's the one hitting hard-working families on lower and middle incomes whilst cutting taxes for millionaires. David Cameron stands for the old divide and rule Tory approach of the past - he can't be the One Nation Prime Minister Britain needs."